I need help with these math problems the subject is Liberal Arts

The equations of three lines are given below.

galben [10]

Answer:

line 1 and 2 = Perpendicular

line 1 and 3 = Perpendicular

line 2 and 3 = Parralel

Step-by-step explanation:

Using Desmos to put in the equations, it shows that it's the answer I provided above.

6 0

3 years ago

Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 o

stepan [7]

Answer:

27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.

Step-by-step explanation:

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$